Quadrupole effects in core and valence photoelectron emission from crystalline germanium measured via a spatially modulated x-ray interference field

Near a crystal x-ray Bragg reflection, the incident and reflected x-ray beams that travel with opposite wave vectors create an x-ray standing-wave (XSW) interference field. The quadrupole (and higher order nondipole) contributions to the photoelectron emission matrix element differ for these two beams due to their different wave vectors. By monitoring the angle-resolved photoelectron yield as a function of photon energy near the (11-1) Bragg back-reflection condition of crystalline Ge, we measure the contribution of nondipole effects to Ge 3p, Ge 3d, and Ge valence-band (4s and 4p) XSW photoelectron emission. Significant changes due to nondipole emission are measured in both the apparent amplitude and phase of the Ge structure factor relative to the true Ge atomic distribution, and compared to theory.